With advances in tissue engineering, the possibility of regenerating injured tissue or failing organs has become a realistic prospect for the first time in medical history. Tissue engineering – the combination of bioactive materials with cells to generate engineered constructs that functionally replace lost and/or damaged tissue – is a major strategy to achieve this goal. One facet of tissue engineering is biofabrication, where three-dimensional tissue-like structures composed of biomaterials and cells in a single manufacturing procedure are generated. Cell-laden hydrogels are commonly used in biofabrication and are termed “bioinks”. Hydrogels are particularly attractive for biofabrication as they recapitulate several features of the natural extracellular matrix and allow cell encapsulation in a highly hydrated mechanically supportive three-dimensional environment. Additionally, they allow for efficient and homogeneous cell seeding, can provide biologically-relevant chemical and physical signals, and can be formed in various shapes and biomechanical characteristics. However, despite the progress made in modifying hydrogels for enhanced bioactivation, cell survival and tissue formation, little attention has so far been paid to optimize hydrogels for the physico-chemical demands of the biofabrication process. The resulting lack of hydrogel bioinks have been identified as one major hurdle for a more rapid progress of the field. In this review we summarize and focus on the deposition process, the parameters and demands of hydrogels in biofabrication, with special attention to robotic dispensing as an approach that generates constructs of clinically relevant dimensions. We aim to highlight this current lack of effectual hydrogels within biofabrication and initiate new ideas and developments in the design and tailoring of hydrogels. The successful development of a “printable” hydrogel that supports cell adhesion, migration, and differentiation will significantly advance this exciting and promising approach for tissue engineering.